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A new discrepancy principle
 J. Math. Anal. Appl
, 2005
"... The aim of this note is to prove a new discrepancy principle. The advantage of the new discrepancy principle compared with the known one consists of solving a minimization problem (see problem (2) below) approximately, rather than exactly, and in the proof of a stability result. To explain this in m ..."
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Cited by 5 (4 self)
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The aim of this note is to prove a new discrepancy principle. The advantage of the new discrepancy principle compared with the known one consists of solving a minimization problem (see problem (2) below) approximately, rather than exactly, and in the proof of a stability result. To explain
Discrepancy principle for DSM II
, 2008
"... Let Ay = f, A is a linear operator in a Hilbert space H, y ⊥ N(A): = {u: Au = 0}, R(A): = {h: h = Au, u ∈ D(A)} is not closed, �fδ − f � ≤ δ. Given fδ, one wants to construct uδ such that limδ→0 �uδ − y � = 0. Two versions of discrepancy principles for the DSM (dynamical systems method) for findin ..."
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Let Ay = f, A is a linear operator in a Hilbert space H, y ⊥ N(A): = {u: Au = 0}, R(A): = {h: h = Au, u ∈ D(A)} is not closed, �fδ − f � ≤ δ. Given fδ, one wants to construct uδ such that limδ→0 �uδ − y � = 0. Two versions of discrepancy principles for the DSM (dynamical systems method
Discrepancy principle for DSM
 I, II, Comm. Nonlin. Sci. and Numer. Simulation
, 2008
"... Let Ay = f, A is a linear operator in a Hilbert space H, y ⊥ N(A): = {u: Au = 0}, R(A): = {h: h = Au,u ∈ D(A)} is not closed, ‖fδ − f ‖ ≤ δ. Given fδ, one wants to construct uδ such that limδ→0 ‖uδ − y ‖ = 0. A version of the DSM (dynamical systems method) for finding uδ consists of solving the pr ..."
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Cited by 7 (6 self)
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the problem ˙uδ(t) = −uδ(t) + T −1 a(t) A ∗ fδ, u(0) = u0, (∗) where T: = A ∗ A, Ta: = T + aI, and a = a(t)> 0, a(t) ց 0 as t → ∞ is suitably chosen. It is proved that uδ: = uδ(tδ) has the property limδ→0 ‖uδ − y ‖ = 0. Here the stopping time tδ is defined by the discrepancy principle: ∫ t 0 e −(t−s) a
L.: A discrepancy principle for Poisson data
 Inverse Problems
, 2010
"... A discrepancy principle for Poisson data ..."
reconstruction and a related discrepancy principle
, 2011
"... Analysis of an approximate model for Poisson data reconstruction and a related discrepancy principle This article has been downloaded from IOPscience. Please scroll down to see the full text article. ..."
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Analysis of an approximate model for Poisson data reconstruction and a related discrepancy principle This article has been downloaded from IOPscience. Please scroll down to see the full text article.
REGULARIZATION AND MOROZOV’S DISCREPANCY PRINCIPLE by
"... A concept of a wellposed problem was initially introduced by J. Hadamard in 1923, who expressed the idea that every mathematical model should have a unique solution, stable with respect to noise in the input data. If at least one of those properties is violated, the problem is illposed (and unstab ..."
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(normally available), in order to solve an illposed problem in a stable fashion. In this thesis, theoretical and numerical investigation of Tikhonov’s (variational) regularization is presented. The regularization parameter is computed by the discrepancy principle of Morozov, and a firstkind integral
The Discrepancy Principle for Choosing Bandwidths in Kernel Density Estimation
, 2012
"... We investigate the discrepancy principle for choosing smoothing parameters for kernel density estimation. The method is based on the distance between the empirical and estimated distribution functions. We prove some new positive and negative results on L1consistency of kernel estimators with bandwi ..."
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We investigate the discrepancy principle for choosing smoothing parameters for kernel density estimation. The method is based on the distance between the empirical and estimated distribution functions. We prove some new positive and negative results on L1consistency of kernel estimators
ON THE GENERALIZED DISCREPANCY PRINCIPLE FOR TIKHONOV REGULARIZATION IN HILBERT SCALES
"... Abstract. For solving linear illposed problems regularization methods are required when the right hand side and the operator are with some noise. In the present paper regularized solutions are obtained by Tikhonov regularization in Hilbert scales and the regularization parameter is chosen by the ge ..."
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Cited by 1 (1 self)
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by the generalized discrepancy principle. Under certain smoothness assumptions we provide order optimal error bounds that characterize the accuracy of the regularized solution. It appears that for getting small error bounds a proper scaling of the penalizing operator B is required. For the computation
A discrepancy principle for equations with monotone continuous operators
 NONLINEAR ANALYSIS
, 2008
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